What are the Properties of rectangular hyperbola?

A rectangular hyperbola is a specific type of hyperbola where the transverse and conjugate axes are equal in length, making it symmetrical about both axes. Its standard equation is (xy = c^2), where (c) is a constant. Key properties include that its asymptotes are perpendicular to each other, and it has a unique feature of having equal distances from the center to the vertices along the axes. Additionally, the slopes of the tangent lines at any point on the hyperbola are negative reciprocals of each other, reflecting its symmetry.